Giovanni Felder

Giovanni Felder (18 November 1958 in Aarau) is a Swiss mathematical physicist and mathematician, working at ETH Zurich. He specializes in algebraic and geometric properties of integrable models of statistical mechanics and quantum field theory.[1]

Giovanni Felder
Giovanni Felder in 2013
Born18 November 1958
Aarau
Alma materETH Zürich
Scientific career
FieldsMathematical Physics
InstitutionsETH Zürich
ThesisRenormalization Group, Tree Expansion, and Non-renormalizable Quantum Field Theories (1986)
Doctoral advisorJürg Martin Fröhlich
Doctoral studentsThomas Willwacher
Websitehttps://people.math.ethz.ch/~felder/

Education and career

Felder attended school in Lugano and Willisau District. He studied physics at ETH Zurich, where he graduated with M.Sc. in 1982 and with Ph.D. in 1986.[2] His doctoral dissertation, entitled Renormalization Group, Tree Expansion, and Non-renormalizable Quantum Field Theories, was supervised by Jürg Fröhlich (and Konrad Osterwalder).[3]

Felder held postdoctoral positions from 1986 to 1988 at IHES, from 1988 to 1989 at the Institute for Advanced Study,[2] and from 1989 to 1991 at the Institute of Theoretical Physics, ETH Zurich.

From 1991 to 1994 he became an assistant professor of mathematics at ETH Zurich. From 1994 to 1996 he worked as professor of mathematics at the University of North Carolina. In 1996 he returned at ETH Zurich as professor of mathematics.[4] From 2013 to 2019, he was the director of the Institute for Theoretical Studies at ETH Zurich.[5]

In 1994 Felder was an invited speaker at the International Congress of Mathematicians in Zurich.[6] He was elected member of the Academia Europaea in 2012[4] and fellow of the American Mathematical Society in 2013.[7]

Research

Felder's research involves mathematical problems motivated by physical ideas.

In the late 1980s Felder did research with Krzysztof Gawedzki and Antti Kupiainen on the geometry of the Wess-Zumino-Witten model in conformal field theory.[8][9] In 1989 he introduced a BRST approach to the "minimal two-dimensional conformal invariant models of Belavin, Polyakov and Zamolodchikov."[10]

With Alexander Varchenko and Vitaly Tarasov, Felder did research on various integrable models[11] in quantum field theory and statistical mechanics and resulting special functions (such as the elliptic gamma function,[12] elliptic quantum groups,[13] and elliptic Macdonald polynomials).[14]

With Alberto Cattaneo in 2000 he gave a path integral interpretation of Kontsevich's deformation quantization of Poisson manifolds[15] as well as a description of the symplectic groupoid integrating a Poisson manifold as an infinite-dimensional symplectic quotient.[16]

He supervised 22 doctoral students as of 2022, including Thomas Willwacher.[3]

References
  1. "Felder, Giovanni, Prof. Dr". ETH Zürich, Mathematics Department.
  2. "Giovanni Felder". Institute for Advanced Study. 9 December 2019.
  3. Giovanni Felder at the Mathematics Genealogy Project
  4. "Giovanni Felder". Academia Europaea.
  5. "50 million Swiss francs to Institute for Theoretical Studies". EurekAlert!, American Association for the Advancement of Science. 15 May 2013.
  6. Chatterji, Srishti Dhar, ed. (1994). Proceedings of the International Congress of Mathematician (PDF). Basel. p. 1247.{{cite book}}: CS1 maint: location missing publisher (link)
  7. "Fellows of the American Mathematical Society". American Mathematical Society. Retrieved 2022-06-18.
  8. Felder, G.; Gawędzki, K.; Kupiainen, A. (1988). "Spectra of Wess-Zumino-Witten models with arbitrary simple groups". Communications in Mathematical Physics. 117 (1): 127–158. Bibcode:1988CMaPh.117..127F. doi:10.1007/BF01228414. S2CID 119767773.
  9. Felder, G.; Gawȩdzki, K.; Kupiainen, A. (1988). "The spectrum of Wess-Zumino-Witten models". Nuclear Physics B. 299 (2): 355–366. Bibcode:1988NuPhB.299..355F. doi:10.1016/0550-3213(88)90288-X.
  10. Felder, Giovanni (1989). "BRST approach to minimal models". Nuclear Physics B. 317 (1): 215–236. Bibcode:1989NuPhB.317..215F. doi:10.1016/0550-3213(89)90568-3.
  11. Felder, Giovanni; Varchenko, Alexander; Tarasov, Vitaly (1996). "Solutions of the elliptic qKZB equations and Bethe ansatz I". arXiv:q-alg/9606005. Bibcode:1996q.alg.....6005F. {{cite journal}}: Cite journal requires |journal= (help)
  12. Felder, Giovanni; Varchenko, Alexander (2000). "The Elliptic Gamma Function and SL(3, Z)⋉Z3  ". Advances in Mathematics. 156: 44–76. arXiv:math/9907061. doi:10.1006/aima.2000.1951. S2CID 16762932.
  13. Felder, Giovanni; Varchenko, Alexander (1996). "On representations of the elliptic quantum group τ,η". Communications in Mathematical Physics. 181 (3): 741–761. arXiv:q-alg/9601003. Bibcode:1996CMaPh.181..741F. doi:10.1007/BF02101296. S2CID 119128058.
  14. Felder, Giovanni; Varchenko, Alexander (2004). "Hypergeometric theta functions and elliptic Macdonald polynomials". International Mathematics Research Notices. 2004 (21): 1037. arXiv:math/0309452. doi:10.1155/S1073792804132893.
  15. Cattaneo, Alberto; Felder, Giovanni (2000). "A Path Integral Approach to the Kontsevich Quantization Formula". Communications in Mathematical Physics. 212 (3): 591–611. arXiv:math/9902090. Bibcode:2000CMaPh.212..591C. doi:10.1007/s002200000229. S2CID 8510811.
  16. Cattaneo, Alberto; Felder, Giovanni (2001), "Poisson sigma models and symplectic groupoids", Quantization of Singular Symplectic Quotients, Basel: Birkhäuser Basel, pp. 61–93, doi:10.1007/978-3-0348-8364-1_4, ISBN 978-3-0348-9535-4, S2CID 10248666, retrieved 2022-06-18
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